Types of Events in Grade XI

Hi students, once again I am here to help you and to teach you an interesting math topic called as types of events in probability of Grade XI. You all have gone through the term probability. It describes the attitude of mind towards some proposition of whose truth we are not certain. Event is the outcome or a combination of outcomes of an experiment. in mathematical terms we can define this as a subset of a sample space. Example:

=> a head in the experiment of tossing a coin is an event.

=> a sum equal to 6 in the experiment of throwing a pair of dice is an event.

Now move to the occurrence of event, with help of an example (see for more Conditional Probability Examples), suppose we throw a die. Let ‘E’ be an event of a perfect number. Then E = 1, 4. Let on the upper most face 3 present. In this we say that event has not occurred. ‘E’ will occur only when 1 and 4 appear on the upper side. In a random problems, if E is the event of a sample space” > sample space S and w in the output. In this situation we can easily say that event E has occurred if w € E. Visit this site for more information on Probability.

Now move to different types of events: 

1. Simple Event

2. Compound Event 

3. Null Event

4. Sure Event or Certain Event

5. Compliment of an event

6. Mutually Exclusive Events 

7. Exhaustive Events 

1) Simple Event: it is defined, If an event has one element of the sample space">sample space. 

S= 1,2,3,4,5,6 

If the event is set of elements less than 2, then

E = 1 is a simple event

2) Compound Event: A compound event is an event which has more than one sample points. 

In the above example, of throwing a die, 1, 4 is a compound event.

3) Null Event (f): As null set is a subset of S, it is also an event called the null event or impossible event.

4) The sample space S= 1, 2, 3, 4, 5, 6 in the above experiment is a subset of S. The event represented by S occurs whenever the experiment is performed. Therefore, the event represented by S is called a sure event or certain event.

5) Complement of an Event: The complement of an event E with respect to S is the set of all the elements of S which are not in E. The complement of E is denoted by E' or EC.

In an experiment if E has not occurred then E' has occurred.

We can easily define union, intersection, complement of events and their properties in types of events.  like: 

 A U B, A ∩ A’ are events of the random experiments.

1. A – B is an event, which is same as “A but not B”.
2. A U B = B U A, A ∩ B, A ∩ B = A ∩ B
3. (A U B)’ = A ∩ B’, (A ∩ B)’ = A’ U B’ 

In upcoming posts we will discuss about Angles and Polygons and Planar cross-sections. Visit our website for information on Karnataka state board books